Abstract

Two effective mathematical approaches based on the probability and statistics theory are proposed for obtaining the oxygen diffusion coefficients in gas-liquid systems. The first method was to apply PLIFI (Planar Laser Induced Fluorescence with Inhibition) to the wake of an isolated bubble rising in water. The chi-squared distribution was introduced to describe the concentration field of oxygen diffusion. The approach provided a feasibility to evaluate the gas-liquid diffusion coefficient by analyzing the temporal evolution of the oxygen spot area on the experimental images. The second method was conducted through a flat air-liquid interface in a Hele-Shaw cell filled with quiescent deoxygenated water. By analogy, the evolution of the oxygen concentration with time was demonstrated to be characterized by the law of inverse gamma. The diffusion coefficient was estimated from the dissolved oxygen concentrations measured by a Clark-type probe at a specific position in the liquid phase. This technique was also tested experimentally for different probe locations to minimize their influence on the diffusion coefficient determination. Moreover, the non-perturbation property of the technique was validated by visualizing the oxygen concentration field around the probe through the colorimetric method. The diffusion coefficients of oxygen in water calculated from the two measurements were almost identical: 2.00 × 10−9 m2 s−1 which is in good agreement with the literature. The specificity of these two methods is that they do not require the properties of the fluid (such as the saturation concentration) or to calibrate the probe. Thus, it provides an alternative approach to evaluate the gas-liquid coefficient accurately and quickly, even in the complex media cases, such as biological media.